Chapter 12, Problem 2CT

To determine

The first five terms of the sequence $a_n=3a_{n-1}+2$ if $a_1=4$.

Answer to Problem 2CT

Solution:

The first five terms of the sequence $a_n=3a_{n-1}+2$ if $a_1=4$ are $4,14,44,134$ and $404$.

Explanation of Solution

Given information:

$a_1=4,a_n=3a_{n-1}+2$

Explanation:

Consider, $a_1=4,a_n=3a_{n-1}+2$.

First term is given which is $a_1=4$.

The second term is $a_2=3a_{2-1}+2$

$\Rightarrow a_2=3a_1+2$

By substituting $a_1=4$,

$\Rightarrow a_2=3\cdot 4+2$

$\Rightarrow a_2=14$

Third term is $a_3=3a_{3-1}+2$

$\Rightarrow a_3=3a_2+2$

By substituting $a_2=14$,

$\Rightarrow a_3=3\cdot 14+2$

$\Rightarrow a_3=44$

Fourth term is $a_4=3a_{4-1}+2$

$\Rightarrow a_4=3a_3+2$

By substituting $a_3=44$,

$\Rightarrow a_4=3\cdot 44+2$

$\Rightarrow a_4=134$

And fifth term is $a_5=3a_{5-1}+2$

$\Rightarrow a_5=3a_4+2$

By substituting $a_4=134$,

$\Rightarrow a_5=3\cdot 134+2$

$\Rightarrow a_5=404$

The first five terms of the sequence $a_n=3a_{n-1}+2$ if $a_1=4$ are $4,14,44,134$ and $404$.